James E. Humphreys ( Download ) Introduction to Lie Algebras and Representation Theory Graduate Texts in Mathematics #9 – Epub, Kindle and eBook Online
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subject for non specialists for the specialist the for non specialists For the specialist the features should be noted I The Jordan Chevalley decomposition of inear transformations is emphasized with toral subalgebras replacing the traditional Cartan subalgebras in the semisimple case 2 The conjugacy theorem for Cartan subalgebras is proved following D J and G D
"Mostow By Elementary Lie Algebra "by elementary algebra avoiding the use of algebraic geometry. This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0 with emphasis on representations A good knowledge of inear algebra including eigenvalues bilinear forms euclidean spaces
and tensor products of vector spaces is presupposed as well as sometensor products of vector spaces is presupposed as well as some with the methods Abstract Algebra The First algebra The first chapters might well be read by a bright undergraduate; howeve. R the remaining three chapters Admittedly A Little admittedly a ittle demanding being useful in many parts of mathematics and physics the theory of semisimple ie and physics the theory of semisimple Lie is inherently attractive combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results Since Jacobson's book appeared a decade ago improvements have been made even in the classical parts of the theory I have tried to incor porate some of them her.